portrait: -10 -6 x(t) = y(t) y(t) =-9.sin(x(t)) - y(t)/5 15 -pi 10 -10 -15 y 1. What are the equilibria for this ODE? 2. What is the Jacobian linearization for this ODE? pi X 10 4. 3. What can you say about the stability of the equilibria based on the linearization? Sketch on the phase portrait the set of initial conditions for which the trajectory converges to (0,0) as time goes to infinity.
portrait: -10 -6 x(t) = y(t) y(t) =-9.sin(x(t)) - y(t)/5 15 -pi 10 -10 -15 y 1. What are the equilibria for this ODE? 2. What is the Jacobian linearization for this ODE? pi X 10 4. 3. What can you say about the stability of the equilibria based on the linearization? Sketch on the phase portrait the set of initial conditions for which the trajectory converges to (0,0) as time goes to infinity.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 4
Consider the following two-dimensional ordinary differential equation together with its phase
portrait:
x(t) = y(t)
y(t) = -9.sin(x(t)) - y(t)/5
15
-pi 10
-10
-15
y
1. What are the equilibria for this ODE?
2. What is the Jacobian linearization for this ODE?
pi
10
3. What can you say about the stability of the equilibria based on the linearization?
4. Sketch on the phase portrait the set of initial conditions for which the trajectory
converges to (0,0) as time goes to infinity.
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